Artificial Neural Networks for the Simulation and Modeling of the Adsorption of Fluoride Ions with Layered Double Hydroxides

Abstract

Adsorption is a complex process since it is affected by multiple variables related to the physicochemical properties of the adsorbate, the adsorbent and the interface; therefore, to understand the adsorption process in batch systems, kinetics, isotherms empiric models are commonly used. On the other hand, artificial neural networks (ANNs) have proven to be useful in solving a wide variety of complex problems in science and engineering due to their combination of computational efficiency and precision in the results; for this reason, in recent years, ANNs have begun to be used for describing adsorption processes. In this work, we present an ANN model of the adsorption of fluoride ions in water with layered double hydroxides (LDHs) and its comparison with empirical kinetic adsorption models. LHD was synthesized and characterized using X-Ray diffraction, FT-Infrared spectroscopy, BET analyses and zero point of charge. Fluoride ion adsorption was evaluated under different experimental conditions, including contact time, initial pH and initial fluoride ion concentration. A total of 262 experiments were conducted, and the resulting data were used for training and testing the ANN model. The results indicate that the ANN can accurately forecast the adsorption conditions with a determination coefficient $R^2$ of 0.9918.

1. Introduction

Adsorption is a surface phenomenon in which a molecule or ion present in a gaseous or liquid bulk phase is transferred to a solid surface followed by their subsequent intraparticle distribution. The adsorption process is complex since there is a very large set of parameters that affect it. These parameters include the adsorbent characteristics (dosage, particle size, specific surface area and porosity) [1]; the adsorbate’s nature, such as the protonation state of a species over the pH, polarity, solubility, initial concentration and molecules size [2]; the physical chemistry of the interface (pH and ionic strength); and the experimental procedure (batch or continues systems, contact time, stirring speed, mixing method and temperature), among others [3].

To understand the adsorption process in batch systems, there are two main approaches. Adsorption kinetics provides valuable information on the rate at which a solute is adsorbed [4]. On the other hand, adsorption isotherms are used mainly in determining the optimum adsorption capacity of adsorbents in equilibrium conditions [5]. Kinetic and isotherm adsorption results are important aspects for the design process and in determining optimization parameters for large-scale adsorption systems [6,7]. However, due to the large collection of empirical kinetic and isothermal models, selecting the appropriate models that best fit the experimental data is challenging; furthermore, while empirical models that use more than two parameters generally provide the best fit, it is well known that these types of models are not easily solved because it is necessary to use nonlinear regression analysis.

Adsorption is a widespread unit operation used for the separation and purification of fluids, including water. The World Health Organization (WHO) describes safe drinking water as water that does not pose any serious health risks during the period of its use [8]. Nearly 200 million people are affected by fluoride-related diseases because of fluoride content in drinking water exceeding the WHO recommendations (1.5 ${\mathrm{m}\mathrm{g}\mathrm{F}}^{-}/\mathrm{L}$) [9]. The main source of fluoride in drinking water is geogenic, and in some regions around the world, the groundwater fluoride concentration ranges up to 20 ${\mathrm{m}\mathrm{g}\mathrm{F}}^{-}/\mathrm{L}$ based on reported studies [9]. Among the various techniques used for the removal of fluoride, the adsorption method stands out as the most widely used for fluoride removal in water due to its notable advantages, such as its affordability, simple design and easy operation [10].

A variety of materials have been reported to be used as adsorbents for fluoride removal, such as carbon-based materials, bauxite, metal–organic frameworks, and layered double hydroxides (LDHs) [11,12,13]. Among these materials, LDHs, with a structural formula expressed as${{[\mathrm{M}}_{1-\mathrm{x}}^{2+}{\mathrm{M}}_{\mathrm{x}}^{3+}{\left(OH\right)}_2]}^{x+}{\left(A^{-n}\right)}_{x/n}·m{H}_2$, have attracted much attention due to their ion-exchange properties, high thermal stability, and acid and alkali resistance [14].

Machine learning (ML) techniques have been used to test the robustness of nonlinear relationships, as in [15], where they conducted a study on a continental scale to rapidly identify soil Cr contamination using visible–near-infrared spectroscopy (vis-NIR) and five machine learning algorithms (LR, SVM, RF, XGBoot and LighGBM).

Moreover, artificial neural networks (ANNs) have recently become popular and helpful models for classification, clustering, pattern recognition and prediction in many fields, including biology, physics, and chemistry [16,17,18]. The term “artificial neural network” refers to a network of nodes that mimics the human brain’s biological neural networks [19]. Different authors have recognized the contribution of artificial neural networks as an alternative to model and simulate the adsorption of inorganic and organic adsorbates. K. Prasad and co-workers [20] focused on acetaminophen adsorption on activated carbon and forecasting the adsorption capacity using an ANN. Cristea et al. [21] fitted the experimental data of oil adsorption on a mixture of carbonized materials with an ANN to predict the sorption capacity. A. Bey and coworkers [22] applied an ANN to model assess the removal efficiency of the ternary dyes adsorption system. These authors found that the ANN model revealed particularly good prediction capability.

To overcome the fact that adsorption efficiency depends on several factors and that there exist several theoretical kinetic models, in this work, we present a neural network model to describe and predict the removal of fluoride ions with an LDH adsorbent material and compare its accuracy with common kinetic theoretical models.

2. Materials and Methods

2.1. Synthesis and Characterization of LDH

LDH synthesis was carried out via the conventional co-precipitation method at low supersaturation, which consisted of the dropwise mixing of a 100 mL solution containing $Mg{\left({NO}_3\right)}_2·6H_{2}O$ and $Al{\left({NO}_3\right)}_3·9H_2$, a second NaOH 1.5 M (100 mL) solution and a third 100 mL ${Na}_2{CO}_3$ 0.2 M solution with 200 rpm magnetic stirring at 30 °C, and the pH of the mixture was maintained at about 10. Then, the product was filtered and washed using deionized water until the filtrate was close to neutral, and finally, the filtered cake was dried at 70 °C for 12 h in an electric oven and ground and passed through a mesh sieve, with the particles between 300 and 710 µm in size.

X-Ray diffraction (XRD) patterns were obtained in the range of 5–80° 2θ at 45 kV and 40 mA, using CuKα1 radiation (λ = 1.5406 Å), with a Malvern-Panalytical X’pertPro diffractometer equipped with a PIXcel detector to study the crystalline properties and identify the identity of the synthesized LDHs.

The Brunauer–Emmett–Teller (BET) surface areas of LDHs were determined by the $N_2$ adsorption–desorption method at 77 K using a surface area analyzer. The BET-specific surface area and mesoporous volume of the LDHs were calculated.

FT-Infrared spectroscopy (FTIR) spectra were recorded on an Agilent Varian 640-IR spectrophotometer. The spectra of the LDHs were recorded between 4000 and 400 ${\mathrm{c}\mathrm{m}}^{-1}$.

The pH of point zero (pHpzc) was determined as follows: An initial 0.1 M NaCl solution was prepared and divided into 50 mL aliquots. Each aliquot was independently adjusted to a pH of 2, 3, 4, 5, 6, 7, 8.9, 10, 11, and up to 12 using a 0.1 M HCl solution or a 0.1 M NaOH solution, as appropriate. Subsequently, 25 mL of each solution was placed in contact with 50 $\mathrm{m}\mathrm{g}$ of each adsorbent material in properly labeled polypropylene vials and stirred at 200 rpm at a constant temperature of 30 °C for 48 h. After that, the pH of each solution was measured with an Orion Star A214 potentiometer and an Orion 8156BNUWP electrode (Thermo Scientific™, Waltham, MA, USA). The tests were performed in duplicate. The results of the final pH values of each sample were graphed against the corresponding initial pH; the pHpzc value is the point where the final pH curve, as a function of the initial pH, intercepts the diagonal line with a slope of 45°.

2.2. Adsorption Experiments in Batch System

A fluorine standard of 1000 ${\mathrm{m}\mathrm{g}\mathrm{F}}^{-}/\mathrm{L}$ was obtained by dissolving 2.21 g of NaF in deionized water. The different desired initial concentrations (10, 20, 30, 40 ${\mathrm{m}\mathrm{g}\mathrm{F}}^{-}/\mathrm{L}$) were prepared with the corresponding aliquots of the standard, and certain volumes of deionized water were added.

The adsorption experiments in the batch system were conducted at a constant temperature of 30 °C and consisted of putting 0.025 g of LDH adsorbent (300–710 µm particle size) in contact with a 10 mL solution of fluoride with different concentrations (10 to 40 ${\mathrm{m}\mathrm{g}\mathrm{F}}^{-}/\mathrm{L}$) and initial pH values (from 4 to 8.5) in polypropylene vials. The contact time varied from 5 to 4000 min.

For measuring the fluoride concentrations in aqueous solutions, a fluoride ion-selective electrode (F-ISE) was used. The amount of fluoride adsorbed $q_t$ (${\mathrm{m}\mathrm{g}\mathrm{F}}^{-}/\mathrm{L}$) at any time $t$ (minutes) was calculated using Equation (1).

$$q_t={\displaystyle \frac{\left(C_0-C_t\right)V}{m}}$$

(1)

where $C_0$ and $C_{\mathrm{t}}$ (${\mathrm{m}\mathrm{g}\mathrm{F}}^{-}/\mathrm{L}$) are the initial fluoride ion concentration and that at time $t$, respectively; $m$ is the mass of the LDH (g); and $V$ is the volume of the solution ($\mathrm{L}$). The adsorption experiments were carried out with two replicates.

2.3. Fitting of Theoretical Kinetic Adsorption Model Experiment Data

There are many references on adsorption kinetics mathematical models to describe adsorption experimental data, including pseudo-first-order (PFO) [23], pseudo-second-order (PSO) [24], Elovich [25], intraparticle diffusion (IPD) [26], pore volume and surface diffusion [27], among others. However, the most commonly applied mathematical models used in solid/liquid systems to describe the adsorption process are the PFO and PSO ones [28,29,30].

The raw experimental adsorption data obtained were fitted with the PFO and PSO models. The PFO and PDO adsorption kinetic models reviewed in this paper are summarized in

Table 1. List of theoretical adsorption kinetic models used in this work.

Model	Nonlinear Form	Description
Pseudo-first-order (PFO)	$q_t=\left(1-e^{-k_{1}t}\right)$	$q_t:$ adsorption capacity at time t ($\mathrm{m}\mathrm{g}/\mathrm{g}$) $q_e:$ equilibrium adsorption capacity ($\mathrm{m}\mathrm{g}/\mathrm{g}$) $t:$ time (min) $k_1:$ first-order rate coefficient (${\mathrm{m}\mathrm{i}\mathrm{n}}^{-1}$)
Pseudo-second-order (PSO)	$q_t={\displaystyle \frac{q_e^2{k}_{2}t}{1+q_e{k}_{2}t}}$	$q_t:$ adsorption capacity at time t ($\mathrm{m}\mathrm{g}/\mathrm{g}$) $q_e:$ equilibrium adsorption capacity ($\mathrm{m}\mathrm{g}/\mathrm{g}$) $t:$ time ($\mathrm{m}\mathrm{i}\mathrm{n})$ $k_2:$ second-order rate coefficient ($\mathrm{g}/(\mathrm{m}\mathrm{g}\ast \min )$)

.

2.4. Fitting of ANN Adsorption Experiment Data

A pattern recognition technique called an artificial neural network (ANN), with the ability to find relationships in given datasets, can be used to explore complex phenomena that are difficult to model analytically [31]. An ANN model learns from experiences or examples (actual input data and corresponding outputs) and has the capacity to generalize the obtained knowledge [32].

The ANN architecture usually is organized into an input layer, one or more hidden layers and an output layer, with each layer containing neurons connected to each other through adjustable synaptic weights, which serve as the memory of the information learned [33,34]. The information is first received by neurons in the input layer, then flows to single or multiple hidden layers to calculate the output of a neuron. Figure 1 illustrates the architecture of the ANN used in this work.

The Python programming language was used during the ANN calculations. The MLPRegressor module (“multi-layer perceptron”) from the scikit library in the Python ecosystem was used. Training and test sets were formed through cross-validation, as supported by the MLPRegressor. To prevent overfitting, we used a 0.1 value in the MLPRegressor hyperparameter validation_fraction, meaning 10% of the training data were used for validation.

The ANN architecture (3-500-500-2), shown in Figure 1, comprised an input layer with three neurons consisting of the initial concentration of fluoride ions $C_i$(${\mathrm{m}\mathrm{g}\mathrm{F}}^{-}/\mathrm{L}$), initial ${pH}_i$ and contact time t (minutes). The number of neurons in the two hidden layers was 500, and finally, there were two neurons in the output layer: adsorption capacity $q_t$ (${\mathrm{m}\mathrm{g}\mathrm{F}}^{-}/\mathrm{L}$) and final pH ${pH}_t$.

The adsorption experimental data were used as inputs to train and validate the ANN model. A total dataset of 262 experiments was split into training and testing data subsets, according to proportions of 75% (129 data) and 25% (43 data); in this case, testing subsets of the data were used for assessing the capability of the trained ANN to make predictions on the adsorption process.

The determination coefficients R² (between outputs and targets) for every theoretical and ANN model were used for assessing the performance of the models in adsorption prediction. In addition to estimating the quality of the prediction, the ANN model was validated using a root-mean-squared error (RMSE) learning curve [35].

3. Results and Discussion

3.1. Synthesis and Characterization of LDH

The powder XRD pattern of the synthesized LDH was recorded, and the result is shown in Figure 2.

It can be seen from Figure 2 that the relative intensities and basal reflections of the LDH sample analyzed include the main planes (003), (006), (009), (015), (018), (110) and (113) at 2θ = 11.5°, 23°, 34.5°, 37°, 45°, 60° and 62°, respectively, which corresponds to the typical patterns of layered double hydroxide structures [36,37].

The N₂ profile adsorption–desorption of the LDH material presented in Figure 3 exhibited a type IV isotherm and H3 hysteresis loop, which suggests that the material has a mesoporous structure (pore size range of 2–50 nm) which is characteristic of a layered structural material [38]. The LDH had a surface area of 110.22 ${\mathrm{m}}^2/\mathrm{g}$, a total pore volume of 0.2703 ${\mathrm{c}\mathrm{m}}^3/\mathrm{g}$, and an average pore diameter of 9.81 nm; similar observations have been reported by [39].

The FTIR spectrum of the LDH in Figure 4 reveals a wide band at about 3510 ${\mathrm{c}\mathrm{m}}^{-1}$ attributed to the stretching vibration of hydroxyl ($-OH$)-linked groups [40]; the two main bands located at around 1640 and 1360 ${\mathrm{c}\mathrm{m}}^{-1}$ correspond to the elongation vibration modes of the water molecules and carbonate anions in the interlamellar space, respectively [41]. The FTIR spectrum contains characteristics bands consistent with those reported in the literature.

The results of the pHpzc determination of the LDH are presented in Figure 5.

As indicated in Figure 5, the pHpzc of the LDH is around 9, which means, theoretically, that the LDH surface is positively charged at a pH below 9; therefore, its surface is negatively charged when the pH is higher than 9.

3.2. Adsorption Experiments in a Batch System

A total of 262 adsorption experiments in the batch system were carried out at different initial fluoride concentrations ($C_i$), initial pH (${pH}_i$) and contact times. The $C_i$ was varied from 10 to 40 ${\mathrm{m}\mathrm{g}\mathrm{F}}^{-}/\mathrm{L}$ to meet the fluoride concentration reported in natural groundwater. For each initial concentration, the initial pH varied with different values in a range from 4 to 8.5. A subset of experimental data of fluoride adsorption is shown in Figure 6.

Figure 6 shows that the adsorption of fluoride ions increased with increasing contact until equilibrium was reached. Further, the increase in fluoride ion concentration resulted in an increase in adsorption capacity at any contact time. Under the initial conditions of 10 ${\mathrm{m}\mathrm{g}\mathrm{F}}^{-}/\mathrm{L}$ and ${pH}_i=$4.0, the experimental equilibrium adsorption capacity was approximately 2.5 ${\mathrm{m}\mathrm{g}\mathrm{F}}^{-}/\mathrm{g}$. A similar result was described by Sarma and Rashid [13], who also studied the adsorption of fluoride on different as-prepared LDH materials, and they reported an equilibrium adsorption capacity of 2.98 ${\mathrm{m}\mathrm{g}\mathrm{F}}^{-}/\mathrm{g}$ at 10 ${\mathrm{m}\mathrm{g}\mathrm{F}}^{-}/\mathrm{L}$ and ${pH}_i=$6.1.

In Figure 6, it can be seen that the increase in the initial pH value resulted in a decrease in adsorption capacity, and the highest fluoride adsorption occurred at an initial pH of 4.0. The influence of aqueous pH on the adsorption capacity might be related to the surface charge of the LDH; at low pH < pHpzc, the surface of the adsorbent is positively charged, due to the protonation of some hydroxyl functional groups ($-OH$) which enhance the interaction with the anionic fluoride [13], which confirms maximum sorption capacity at pH 4.0 that decreases at higher pH values.

3.3. Fitting of Results of Theoretical Kinetic Adsorption Model Experiments

The PFO and PSO models were used to fit the experimental data of fluoride ion adsorption onto the LDH material. The PFO and PSO parameters (rate constants $k_1$ and $k_2$ and $q_e$ calculated values) and the determination coefficients of fitting $R^2$obtained in the nonlinear regression are given in

Table 2. Kinetic parameters of PFO and PSO models of fluoride ion removal by LDH at 30 °C.

Experimental Conditions	PFO			PSO
	${\mathit{k}}_1$ (${\mathbf{\times }\mathbf{10}}^{\mathbf{3}}$)	${\mathit{q}}_{\mathit{e}}$${\mathbf{m}\mathbf{g}\mathbf{F}}^{-}/\mathbf{g}$	${\mathit{R}}^2$	${\mathit{k}}_2$ (${\mathbf{\times }\mathbf{10}}^{\mathbf{3}}$)	${\mathit{q}}_{\mathit{e}}$${\mathbf{m}\mathbf{g}\mathbf{F}}^{-}/\mathbf{g}$	${\mathit{R}}^2$
$C_i$ $=10{\mathrm{m}\mathrm{g}\mathrm{F}}^{-}/\mathrm{L}$$,{pH}_i$ = 4.0	0.987	2.94	0.9709	0.362	3.4748	0.9708
$C_i$ $=10{\mathrm{m}\mathrm{g}\mathrm{F}}^{-}/\mathrm{L}$$,{pH}_i$ = 7.0	3.02	2.25	0.9438	1.83	2.4554	0.9635
$C_i$ $=10{\mathrm{m}\mathrm{g}\mathrm{F}}^{-}/\mathrm{L}$$,{pH}_i$ = 7.5	3.01	2.23	0.9398	1.83	2.4421	0.9611
$C_i$ $=10{\mathrm{m}\mathrm{g}\mathrm{F}}^{-}/\mathrm{L}$ $,{pH}_i$ = 8.0	2.86	2.17	0.9202	2.01	2.3448	0.9404
$C_i$ $=10{\mathrm{m}\mathrm{g}\mathrm{F}}^{-}/\mathrm{L}$$,{pH}_i$ = 8.3	3.37	2.02	0.9020	2.69	2.1371	0.9214
$C_i$ $=10{\mathrm{m}\mathrm{g}\mathrm{F}}^{-}/\mathrm{L}$$,{pH}_i$ = 8.5	1.82	2.05	0.9751	1.01	2.3461	0.9863
$C_i$ $=20{\mathrm{m}\mathrm{g}\mathrm{F}}^{-}/\mathrm{L}$$,{pH}_i$ = 4.0	4.09	5.06	0.9553	1.18	5.4430	0.9762
$C_i$ $=20{\mathrm{m}\mathrm{g}\mathrm{F}}^{-}/\mathrm{L}$$,{pH}_i$ = 6.0	1.96	5.10	0.9550	0.437	5.7774	0.9519
$C_i$ $=20{\mathrm{m}\mathrm{g}\mathrm{F}}^{-}/\mathrm{L}$$,{pH}_i$ = 6.5	2.16	4.94	0.9810	0.480	5.6050	0.9816
$C_i$ $=20{\mathrm{m}\mathrm{g}\mathrm{F}}^{-}/\mathrm{L}$$,{pH}_i$ = 7.0	2.13	4.92	0.9680	0.506	5.5429	0.9701
$C_i$ $=20{\mathrm{m}\mathrm{g}\mathrm{F}}^{-}/\mathrm{L}$$,{pH}_i$ = 7.5	2.26	4.91	0.9784	0.537	5.5203	0.9774
$C_i$ $=20{\mathrm{m}\mathrm{g}\mathrm{F}}^{-}/\mathrm{L}$$,{pH}_i$ = 8.0	4.34	4.17	0.9458	1.53	4.4231	0.9653
$C_i$ $=20{\mathrm{m}\mathrm{g}\mathrm{F}}^{-}/\mathrm{L}$$,{pH}_i$ = 8.3	4.21	3.99	0.9217	1.67	4.2096	0.9489
$C_i$ $=20{\mathrm{m}\mathrm{g}\mathrm{F}}^{-}/\mathrm{L}$$,{pH}_i$ = 8.5	3.56	3.64	0.9175	1.58	3.8420	0.9393
$C_i$ $=40{\mathrm{m}\mathrm{g}\mathrm{F}}^{-}/\mathrm{L}$$,{pH}_i$ = 4.0	22.8	6.98	0.8645	3.71	7.4678	0.9358
$C_i$ $=40{\mathrm{m}\mathrm{g}\mathrm{F}}^{-}/\mathrm{L}$$,{pH}_i$ = 8.5	17.6	6.36	0.8522	2.96	6.8707	0.9260

.

As can be seen from Table 2, based on the determination coefficients of fitting for both models, it seems that two models adequately describe the kinetics. However, for all the experiments, the PSO has the highest $R^2$ values; this indicates the applicability of the PSO kinetic model to describe the adsorption process. The PSO model is commonly associated with covalent bonding between the adsorbent and adsorbate (chemisorption) [42]. The determination coefficients for PSO varied from 0.9214 to 0.9863 for the worst and best fit, respectively.

Table 2 shows that the $k_1$, $k_2$ and $q_e$ parameter values of the PFO and PSO models are affected by the initial pH and concentrations. The influence of pH and $C_i$on the model parameter values has not yet been theoretically studied due to its complexity, since numerous other different factors can vary from one system to another [43].

3.4. Fitting of ANN Adsorption Experimental Data

The ANN model described in Section 2.4 was trained and tested with the use of the adsorption in the batch system experimental data.

In the prediction of fluoride ion adsorption, the ANN model obtained a good relationship (between the experimental data and the predicted values) from the testing data subset; the $R^2$ values obtained were 0.9918 and 0.9585 for $q_t$and ${pH}_f$, respectively. Figure 7a,b show the predicted values against the experimental values of $q_t$and ${pH}_f$ and the accuracy of the prediction of the ANN model in terms of $R^2$.

To assess the learning performance of the ANN model, a learning curve was generated using the calculated accuracy (in terms of RMSE) according to a given training sample size. The learning curve is plotted in Figure 8.

The learning curve presented in Figure 8 shows how the ANN model predictions improve as the number of training examples increases, but the large RMSE gap between training and testing indicates that the model has some difficulties in generalizing unseen data. A solution to improve this behavior may be to add more data to our training dataset in future works. Furthermore, it can be observed that as the training set size increases, the training and testing RMSE lines approach each other and tend to converge.

In contrast to the observations made with the empirical PFO and PSO models, the ANN can predict the fluoride ion removal behavior at different $t$, $C_i\mathrm{and}$ ${pH}_i$ values. Once the ANN model was trained and tested, we used it to interpolate and predict the response variables $q_t$ and ${pH}_f$ within the range of values of the independent variables $t$, $C_i$ and ${pH}_i$with which the model was trained. Figure 9 and Figure 10 show a surface plot of the predicted $q_t$ and ${pH}_f$ with different independent variables.

In Figure 9, it can be observed that with an increase in time and at any initial pH value, the final pH tends to be around a value close to 9, which agrees with the Phpzc value obtained experimentally.

Figure 10 shows that the trend shown by the experimental data on the increase in adsorption capacity when the initial concentration increases is reflected in the values required by the ANN model.

Modeling adsorption kinetics is essential to describe the experimental data and to interpolate the results for conditions beyond those acquired experimentally, in other words, generalize the obtained knowledge.

Once the trained ANN model was capable of describing the kinetic adsorption process, it was used to predict adsorption capacity at equilibrium time (1440 min), and the surface plot obtained is presented in Figure 11.

According to the results reported in Figure 11, with an increasing initial concentration of fluoride ions, the maximum adsorption of fluoride ions occurred at 40 ${\mathrm{m}\mathrm{g}\mathrm{F}}^{-}/\mathrm{L}$. We obtained a negative effect with an increase in pH, with an optimum value at 4.0. In the surface plot (Figure 11), for the profile ($C_i$ vs. $q_e$), you can see the characteristic curve of adsorption kinetics, which is replicated along the z axis (pH), forming a mantle in the three dimensions. It can be seen how the two levels interact for the factors (${pH}_i$ and $C_i$) and their influence on the concentration at equilibrium.

4. Conclusions

The LDH material was synthetized using the coprecipitation method. According to XRD, FTIR, BET surface area and pHpzc analyses, a material with the expected characteristics was obtained: LDH was used for the removal of fluoride ions from water in different experimental conditions, and a total of 262 experimental data were used to train and test the artificial neural network model. Based on the determination coefficients obtained ($R^2$ = 0.9918 and $R^2$ = 0.9585 for adsorption capacity and final pH, respectively), the ANN model prediction gave a better result compared to that obtained with the empirical PFO and PSO models, which varied from 0.9214 to 0.9863. The ANN-trained model allows us to predict the optimal adsorption conditions, which resulted in ${pH}_{\mathit{i}}$ = 4.0 and ${\mathit{C}}_{\mathit{i}}$ = 40 ${\mathrm{m}\mathrm{g}\mathrm{F}}^{-}/\mathrm{L}$. It was possible to determine the effect of pH on the adsorption process through ANN, which has not been reported with the most used empirical models.